Problem: The following line passes through point $(-4, 3)$ : $y = -\dfrac{3}{7} x + b$ What is the value of the $y$ -intercept $b$ ?
Solution: Substituting $(-4, 3)$ into the equation gives: $3 = -\dfrac{3}{7} \cdot -4 + b$ $3 = \dfrac{12}{7} + b$ $b = 3 - \dfrac{12}{7}$ $b = \dfrac{9}{7}$ Plugging in $\dfrac{9}{7}$ for $b$, we get $y = -\dfrac{3}{7} x + \dfrac{9}{7}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(-4, 3)$